{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ***Introduction to Radar Using Python and MATLAB***\n",
    "## Andy Harrison - Copyright (C) 2019 Artech House\n",
    "<br/>\n",
    "\n",
    "# Probability of Detection with Rayleigh Noise\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Referring to Section 6.1.3, for coherent detectors, illustrated in Figure 5.11, the noise is modeled  at the output of the in-phase and quadrature channels as Gaussian, with zero mean and noise power of $\\sigma^2/2$.  The magnitude of the in-phase and quadrature channels is (Equation 6.12)\n",
    "\n",
    "$$\n",
    "    z = \\sqrt{X_I^2 + X_Q^2},\n",
    "$$\n",
    "\n",
    "then the resulting probability density function follows a Rayleigh distribution given by (Equation 6.13)\n",
    "\n",
    "$$\n",
    "    p(z) = \\frac{z}{\\sigma^2}\\, \\exp\\left(\\frac{-z^2}{2\\sigma^2}\\right).\n",
    "$$\n",
    "\n",
    "Following the procedure in  Section 6.1.2, the probability of false alarm for the coherent detector is written as (Equation 6.14)\n",
    "\n",
    "\n",
    "$$\n",
    "    P_{{fa}} = \\int\\limits_{V_T}^\\infty \\frac{z}{\\sigma^2}\\, \\exp\\left(-\\frac{z^2}{2\\sigma^2}\\right)\\, dz = \\exp\\left(-\\frac{V_T^2}{2\\sigma^2}\\right).\n",
    "$$\n",
    "\n",
    "Solving for the detection threshold gives (Equation 6.15)\n",
    "\n",
    "$$\n",
    "    V_T = \\sqrt{-2\\sigma^2 \\ln{(P_{{fa}}})}.\n",
    "$$\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Begin by getting the library path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import lib_path"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the start and end signal to noise ratio (dB)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "snr_start = 0.0\n",
    "\n",
    "snr_end = 20.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the signal to noise array using the `linspace` routine from `scipy`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import linspace\n",
    "\n",
    "snr = 10.0 ** (linspace(snr_start, snr_end, 200) / 10.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the probability of false alarm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "pfa = 1e-6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calcualte the probability of detection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from Libs.detection.single_pulse import pd_rayleigh\n",
    "\n",
    "pd = pd_rayleigh(snr, pfa)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Display the probability of detection for Rayleigh noise using the `matplotlib` routines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "\n",
    "from numpy import log10\n",
    "\n",
    "\n",
    "\n",
    "# Set the figure size\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = (15, 10)\n",
    "\n",
    "\n",
    "\n",
    "# Display the results\n",
    "\n",
    "plt.plot(10.0 * log10(snr), pd, '')\n",
    "\n",
    "\n",
    "\n",
    "# Set the plot title and labels\n",
    "\n",
    "plt.title('Pd - Rayleigh Noise', size=14)\n",
    "\n",
    "plt.xlabel('Signal to Noise (dB)', size=12)\n",
    "\n",
    "plt.ylabel('Probability of Detection', size=12)\n",
    "\n",
    "\n",
    "\n",
    "# Set the tick label size\n",
    "\n",
    "plt.tick_params(labelsize=12)\n",
    "\n",
    "\n",
    "\n",
    "# Turn on the grid\n",
    "\n",
    "plt.grid(linestyle=':', linewidth=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
